Abū
al-Wafāʾ, Muḥammad ibn Muḥammad ibn Yaḥyā ibn Ismāʿīl ibn al-ʿAbbās al-Būzjānī
or Abū al-Wafā Būzhgānī (Persian:
ابوالوفا بوزجانی or بوژگانی)
(10 June 940 – 15 July 998) was a Persian
mathematician and astronomer
who worked in Baghdad. He made important innovations in spherical trigonometry, and his work on arithmetics
for businessmen contains the first instance of using negative
numbers in a medieval Islamic text.
He
is also credited with compiling the tables of sines and tangents at 15'
intervals. He also introduced the secant and cosecant functions, as well
studied the interrelations between the six trigonometric lines associated with
an arc. His Almagest was widely read by medieval Arabic astronomers in
the centuries after his death. He is known to have written several other books
that have not survived.
Abu Al-Wafa' was the first to build a wall quadrant to observe the sky.[4]
It has been suggested that he was influenced by the works of Al-Battani
as the latter describes a quadrant instrument in his Kitāb az-Zīj. His
use of tangent helped to solve problems involving
right-angled spherical triangles, and developed a new
technique to calculate sine
tables, allowing him to construct more accurate tables than his predecessors.
In 997, he participated in an experiment to determine the
difference in local time between his location and that of al-Biruni (who was
living in Kath, now a part of Uzbekistan). The result was very close to present-day
calculations, showing a difference of approximately 1 hour between the two
longitudes. Abu al-Wafa is also known to have worked with Abū Sahl al-Qūhī, who was a famous maker of
astronomical instruments. While what is extant from his works lacks theoretical
innovation, his observational data were used by many later astronomers,
including al-Biruni's
He established several trigonometric identities such as sin(a
± b) in their modern form, where the Ancient Greek
mathematicians had expressed the equivalent identities in terms of chords.
where A, B, C are the sides
(measured in radians) and a, b, c are the opposing angles.
Some sources suggest that he introduced the tangent function, although other sources
give the credit for this innovation to al-Marwazi.
If Persian mathematician Abu al-Wafa’ al-Buzjani were alive
today, he’d be 1075 years old. It’s startling, then, to consider the importance
of his work, conceived of and produced so many years ago.
Today’s doodle honors this man, an innovator whose
contributions to science include one of the first known introductions to
negative numbers, and the development of the first quadrant, a tool used by
astronomers to examine the sky. His pioneering work in spherical
trigonometry was hugely influential for both mathematics and
astronomy.
In our innovative society, we don’t always stop to reflect on
the historical figures whose work makes our own advances possible. Abu
al-Wafa’s legacy demonstrates the monumental importance of some of history’s
lesser known scientists. His picture may not be pinned to the wall in
elementary school classrooms, but it’s now pinned to the homepage of
Google.com. Happy 1075th, Abu al-Wafa al-Buzjani!
